Quantum treatment of cosmological axion perturbations

We carefully investigate the time evolution of the density perturbation in a universe dominated by a scalar field which we regard as the conventional (invisible) axion. Although we employ the nonrelativistic approximation for the axion field, we treat it fully quantum theoretically, differing from the conventional analysis. We find the Jeans length of O(1/ H), where m is the axion mass and H the Hubble parameter, in accordance with the previous estimate in the literature. Considering a universe dominated by classical radiation and axions, we explicitly give the analytic solution for the isocurvature-type perturbation. Our quantum treatment allows a new interpretation that the Jeans instability can be viewed as induced particle creation in an expanding background. In particular, we find there exists a contribution of spontaneous particle creation from the vacuum to the density perturbation, though the amplitude is very small. We also discuss the effect of a self-interaction and find that it is unimportant in the cosmological context if the scalar field is the axion, but can change the Jeans length considerably if it is some other field which has a stronger interaction than the axion.